Solve {left(9/32right)}^5+27/32-1

$${ \left( \frac{ 9 }{ 32 } \right) }^{ 5 } + \frac{ 27 }{ 32 } -1$$

Evaluate

$$-\frac{5183831}{33554432}\approx -0.154490203$$

Solution Steps

Calculate \frac{9}{32} to the power of 5 and get \frac{59049}{33554432}.

$$\frac{59049}{33554432}+\frac{27}{32}-1$$

Least common multiple of 33554432 and 32 is 33554432. Convert \frac{59049}{33554432} and \frac{27}{32} to fractions with denominator 33554432.

$$\frac{59049}{33554432}+\frac{28311552}{33554432}-1$$

Since \frac{59049}{33554432} and \frac{28311552}{33554432} have the same denominator, add them by adding their numerators.

$$\frac{59049+28311552}{33554432}-1$$

Add 59049 and 28311552 to get 28370601.

$$\frac{28370601}{33554432}-1$$

Convert 1 to fraction \frac{33554432}{33554432}.

$$\frac{28370601}{33554432}-\frac{33554432}{33554432}$$

Since \frac{28370601}{33554432} and \frac{33554432}{33554432} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28370601-33554432}{33554432}$$

Subtract 33554432 from 28370601 to get -5183831.

$$-\frac{5183831}{33554432}$$

Factor

$$-\frac{5183831}{33554432} = -0.15449020266532898$$